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605

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 605

Source:

5/4/2010
Let f(x)f(x) be a differentiable function. Find the following limit value:
lim⁡n→∞(nk){f(xn)−f(0)}k.\lim_{n\to\infty} \dbinom{n}{k}\left\{f\left(\frac{x}{n}\right)-f(0)\right\}^k.
Especially, for f(x)=(x−α)(x−β)f(x)=(x-\alpha)(x-\beta) find the limit value above.
1956 Tokyo Institute of Technology entrance exam
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